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The 12 inch base of a right triangle is growing at 3 inches per hour, and the 16 inch height is shrinking at 3 inches per hour.
a. Is the area increasing or decreasing?
b. Is the perimeter increasing or decreasing?
c. Is the hypotenuse increasing or decreasing?
2. Lava flowing from a hole at the top of a hill is forming a conical mountain whose height is always the same as the width of its base (Figure). If the mountain is increasing in height at 2 feet per hour when it is 500 feet high, how fast is the lava flowing (how fast is the volume of the mountain increasing)? ( V = 1/3 πr2h)
3. The string of a kite is perfectly taut and always makes an angle of 35o above horizontal.
a. If the kite flyer has let out 500 feet of string, how high is the kite?
b. If the string is let out at a rate of 10 feet per second, how fast is the kite's height increasing?
Describe how the Fibonacci Numbers are related to the Golden Ratio. Also define the rigid motion "glide reflection."
A company that manufactures laser printers for computers has monthly fixed costs of $177,000 and variable costs of $650 per unit produced. The company sells the printers for $1,250 per unit. How many printers must be sold each month for the compan..
Find (and describe) all the regular tessellations of the plane. Note that septagons, nonagons, and 11-gons are not provided. How do you know each one you find really fills in all the gaps around a vertex point? How do you know when you're done?
These questions are about the quadratic function which takes the form: Choose the false statements.
Show that the above system of equations can be derived from the Law of Mass Action. Do this by finding reactions that give rise to these equations.Also, assumptions are made about the rate constants to obtain these equations and you should make sure ..
Express the function in the form f(x) = a(x-h)2 + K and indicate the vertex. An object is thrown upward from the top of a 160-foot (Ho) building with an initial velocity (Vo) of 48 feet per second. How long after the object is projected upward wil..
1. Contrast and compare the supply chains required for the private label eBags and those drop-shipped directly from the manufacturers. Answer in the context of the case. 2. If eBags were to enter the footwear business, what new supply chain managemen..
Let L and M be lines in the xy-plane. Prove that L is equipotent to M or in other words that they are in one to one correspondence.
A farmer Wants to fence a rectangular yard using 260 ft of fencing. What dimensions should he use for the greatest area?
Given a set of all real numbers containing 4s and 5s in their decimal representation. Determine the given set is countable or uncountable.
Y"+2y'+10y=6sin2x is the mathmatical model for a mechanical vibrating system. The steady state solution is? a) z=C1e^-xcos3x+C2e^-xsin3x b)z=C1e^-xcos3x+C2e^-xsin3x-12cos2x+18sin2x c) z=18sin2x-12cos2x d)z=3sin2x+2cos2x e) none of the above
A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume. Assume cross section is square.
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